Do I automatically get a LISL offer (if I do not accept the lease modification and my lease expires) or am I required to begin to pay the rent the City has determined?

That will be entirely up to the City. If they want to keep you on your lease, they’ll give you an additional extension and you’ll pay rent based on the current lease, or you’ll get LISL per the old lease terms, or you may stay on as a tenant of the City on a rental basis.